MET Most Repeated Questions with Answers – Physics, Chemistry & Maths

High Weightage Chapters of MET 2027

Focus on the following high-weightage chapters to prioritise your MET 2027 preparation and maximise your score.

MET Most Scoring Topics in Physics

MET Most Scoring Topics in Chemistry

MET Most Scoring Topics in Mathematics

MET Important Questions with Answers 2027

The MET paper covers questions from physics, chemistry, and mathematics for B.Tech students. Candidates should not learn questions. Instead, they should understand the concepts behind these questions and practise different variations, because the same concepts repeat in the exam again and again.

MET Physics Most Repeated Questions

Question 1: In the equation $\mathrm{P}=\mathrm{b}\left(\mathrm{x} / \mathrm{t}^2-\mathrm{a}\right)$, where P is pressure, x is distance, and t is time, what are the dimensions of a/b?

(A) $\mathrm{MLT}^{-2}$

(B) $\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}$

(C) $\mathrm{ML}^{-2} \mathrm{~T}^2$

(D) $\mathrm{M}^{-1} \mathrm{LT}^2$

Correct Answer: B. $\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}$

Solution:

Since $\mathrm{x} / \mathrm{t}^2$ and a are subtracted, both must have the same dimensions.

Dimensions of a $=\mathrm{LT}^{-2}$

Pressure has dimensions $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$.

From $\mathrm{P}=\mathrm{b} \times \mathrm{a}$ :

Dimensions of $\mathrm{b}=\mathrm{ML}^{-2}$

Therefore,

Dimensions of $\mathrm{a} / \mathrm{b}=\left(\mathrm{LT}^{-2}\right) /\left(\mathrm{ML}^{-2}\right)$

$=\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}$

Question 2: The coordinates of a particle are x = at² and y = bt². What is the speed of the particle at time t?

(A) $2 \mathrm{t}(\mathrm{a}+\mathrm{b})$

(B) $2 \mathrm{t} \sqrt{ }\left(\mathrm{a}^2+\mathrm{b}^2\right)$

(C) $\mathrm{t} \sqrt{ }\left(\mathrm{a}^2+\mathrm{b}^2\right)$

(D) $2 \sqrt{ }\left(\mathrm{a}^2+\mathrm{b}^2\right)$

Correct Answer: B. $2 \mathrm{t} \sqrt{ }\left(\mathrm{a}^2+\mathrm{b}^2\right)$

Solution:

Velocity in the x-direction:

$\mathrm{vx}=\mathrm{dx} / \mathrm{dt}=2 \mathrm{at}$

Velocity in the y-direction:

vy = dy/dt = 2bt

Speed $=\sqrt{ }\left(v x^2+v y^2\right)$

$=\sqrt{4a^2t^2+4b^2t^2}$

$=2t\sqrt{a^2+b^2}$

Question 3: The force required to move a body up an inclined plane is twice the force required to prevent it from sliding down. If μ is the coefficient of friction, what is the inclination of the plane?

A. tan⁻¹(μ)
B. tan⁻¹(2μ)
C. tan⁻¹(3μ)
D. tan⁻¹(μ/3)

Correct Answer: C. tan⁻¹(3μ)

Solution:

Force required to move the body upward:

$F_1=m g \sin \theta+\mu m g \cos \theta$

Force required to prevent downward sliding:

$\mathrm{F}_2=\mathrm{mg} \sin \theta-\mu \mathrm{mg} \cos \theta$

Given:

$F_1=2 F_2$

Therefore:

$\mathrm{mg} \sin \theta+\mu \mathrm{mg} \cos \theta=2 \mathrm{mg} \sin \theta-2 \mu \mathrm{mg} \cos \theta$

So,

$3 \mu \mathrm{mg} \cos \theta=\mathrm{mg} \sin \theta$

Therefore:

$\tan \theta=3 \mu$

Hence,

$\theta=\tan ^{-1}(3 \mu)$

Question 4: he power generated by a wind turbine is proportional to which power of the wind speed v?

A. v
B. v²
C. v³
D. v⁴

Correct Answer: C. v³

Solution:

The kinetic energy of air is proportional to v². The amount of air passing through the turbine per unit time is proportional to v.

Therefore:

Power $\propto v^2 \times v$

So, Power $\propto V^3$

Question 5: A sphere of mass m moving with velocity u collides head-on with another stationary sphere of the same mass. If the coefficient of restitution is e, what is the ratio of their speeds after collision?

A. (1 + e)/(1 − e)
B. (1 − e)/(1 + e)
C. 1 − e²
D. 1 + e²

Correct Answer: B. (1 − e)/(1 + e)

Solution:

Using conservation of momentum:

$u=v_1+v_2$

Using the coefficient of restitution:

$e=\left(v_2-v_1\right) / u$

Therefore:

$v_1=\frac{u(1-e)}{2}$

$v_2=\frac{u(1+e)}{2}$

Hence:

$v_1 / v_2=(1-e) /(1+e)$

Question 6: A uniform pencil of length L is initially vertical and falls about one end. What is its angular velocity just before it becomes horizontal?

A. $\sqrt{ }(3 g / L)$

B. $\sqrt{ }(6 \mathrm{~g} / \mathrm{L})$

C. $\sqrt{ }(2 \mathrm{~g} / \mathrm{L})$

D. $\sqrt{ }(\mathrm{g} / \mathrm{L})$

Correct Answer: A. $\sqrt{ }(3 g / L)$

Solution:

The centre of mass falls through a distance L/2.

Loss of potential energy:

= mgL/2

Moment of inertia of the pencil about one end:

$\text { I = mL²/3 }$

Using conservation of energy:

$\mathrm{mgL} / 2=1 / 2 \times \mathrm{mL}^2 / 3 \times \omega^2$

Solving:

$\omega^2=3 \mathrm{~g} / \mathrm{L}$

Therefore:

$\omega=\sqrt{ }(3 g / L)$

Question 7: A solid sphere of radius R is struck at a point at height h above its centre. If it acquires a translational speed v₀, what is its angular velocity immediately after the impulse?

A. $5 h v_0 /\left(2 R^2\right)$
B. $2 h v_0 /\left(5 R^2\right)$
C. $5 \mathrm{v}_0 /(2 \mathrm{hR})$
D. $2 \mathrm{Rv}_0 /(5 \mathrm{~h})$

Correct Answer: A. $5 h v_0 /\left(2 R^2\right)$

Solution:

For a solid sphere:

$\mathrm{I}=2 \mathrm{mR}^2 / 5$

The impulse gives the sphere linear momentum:

$\mathrm{J}=\mathrm{mv}_0$

Angular impulse about the centre:

$\mathrm{I} \omega=\mathrm{Jh}$

Therefore:

$\left(2 m R^2 / 5\right) \omega=m v_0 h$

So,

$\omega=5 h v_{\mathrm{o}} /\left(2 \mathrm{R}^2\right)$

Question 8: Two masses M and m are initially at a very large distance from each other with negligible relative velocity. What is their relative speed when their separation becomes d?

A. $\sqrt{ }(\mathrm{GMm} / \mathrm{d})$

B. $\sqrt{ }(2 \mathrm{G}(\mathrm{M}+\mathrm{m}) / \mathrm{d})$

C $\sqrt{ }(\mathrm{G}(\mathrm{M}+\mathrm{m}) /(2 \mathrm{~d}))$

D $2 \mathrm{G}(\mathrm{M}+\mathrm{m}) / \mathrm{d}$

Correct Answer: B. $\sqrt{ }(2 \mathrm{G}(\mathrm{M}+\mathrm{m}) / \mathrm{d})$

Solution:

Using conservation of energy:

$\mathrm{GMm} / \mathrm{d}=1 / 2 \times[\mathrm{Mm} /(\mathrm{M}+\mathrm{m})] \times \mathrm{v}^2$

Solving for v:

$\mathrm{v}^2=2 \mathrm{G}(\mathrm{M}+\mathrm{m}) / \mathrm{d}$

Therefore:

$v=\sqrt{ }[2 G(M+m) / d]$

Question 9: A cylinder of mass M and density ρ is completely immersed in a liquid of density σ. If the vessel has cross-sectional area A, what is the increase in pressure at the bottom due to the cylinder?

A. Mg/A
B. Mσg/(ρA)
C. Mρg/(σA)
D. σg/(ρA)

Correct Answer: B. Mσg/(ρA)

Solution:

Volume of the cylinder:

$V=M / \rho$

Buoyant force:

$F=\sigma V g$

Therefore:

$\text { F = M } \sigma \mathrm{g} / \rho$

Pressure increase:

$\Delta \mathrm{P}=\mathrm{F} / \mathrm{A}$

Hence:

$\Delta P=M \sigma g /(\rho A)$

Question 10: An AC circuit has V = 100 sin ωt and I = 100 sin(ωt + π/3) mA. What is the average power consumed?

A. 2.5 W
B. 5 W
C. 25 W
D. 50 W

Correct Answer: A. 2.5 W

Solution:

Phase difference $=60^{\circ}$

RMS voltage $=100 / \sqrt{2} \mathrm{~V}$

RMS current $=0.1 / \sqrt{2} \mathrm{~A}$

Average power:

$P=V_{\mathrm{rms}}\times I_{\mathrm{rms}}\times\cos60^\circ$

$P=\left(\frac{100}{\sqrt{2}}\right)\times\left(\frac{0.1}{\sqrt{2}}\right)\times\frac{1}{2}$

Therefore:

$\mathrm{P}=2.5 \mathrm{~W}$

MET Chemistry Most Repeated Questions

Question 1: Which of the following molecules has a linear shape?

A. H₂O
B. NH₃
C. CO₂
D. CH₄

Correct Answer: C. CO₂

Solution:

In CO₂, the central carbon atom has two bond pairs and no lone pair. According to VSEPR theory, the two bond pairs arrange themselves at 180°.

Therefore, CO₂ has a linear shape.

Question 2: What is the coordination number of the central metal ion in $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_3$?

A. 3
B. 4
C. 6
D. 9

Correct Answer: C. 6

Solution:
There are six NH₃ ligands directly attached to the cobalt ion.

Therefore, the coordination number is: 6

Question 3: For a first-order reaction, what is the unit of the rate constant?

A. mol L⁻¹ s⁻¹
B. L mol⁻¹ s⁻¹
C. s⁻¹
D. mol² L⁻² s⁻¹

Correct Answer: C. s⁻¹

Solution:
For a first-order reaction:

Rate = k[A]

Therefore:

k = Rate/[A]

The unit of k is s⁻¹.

Question 4: Which equation is used to calculate the cell potential under non-standard conditions?

A. Arrhenius equation
B. Nernst equation
C. Henderson equation
D. Clausius equation

Correct Answer: B. Nernst equation

Solution:
The Nernst equation relates electrode or cell potential to concentration under non-standard conditions.

At 298 K:

E = E° − (0.0591/n) log Q

Therefore, the correct answer is the Nernst equation.

Question 5: Which factor changes the value of the equilibrium constant of a reaction?

A. Concentration
B. Pressure
C. Catalyst
D. Temperature

Correct Answer: D. Temperature

Solution:
The value of the equilibrium constant depends only on temperature.

Changing concentration or pressure may shift the equilibrium position, but it does not change K at a fixed temperature.

Question 6: Which reagent is commonly used to test for the presence of an aldehyde?

A. Tollens' reagent
B. NaCl
C. HCl
D. NaOH

Correct Answer: A. Tollens' reagent

Solution:
Aldehydes reduce Tollens' reagent and produce a silver mirror.

Therefore, Tollens' reagent is commonly used to distinguish aldehydes from ketones.

Question 7: Which of the following is a monosaccharide?

Options:

A. Sucrose
B. Glucose
C. Starch
D. Cellulose

Correct Answer: B. Glucose

Solution:
Glucose is a simple sugar containing one sugar unit, so it is a monosaccharide.

Sucrose is a disaccharide, while starch and cellulose are polysaccharides.

Question 8: Which thermodynamic quantity represents the heat content of a system at constant pressure?

A. Entropy
B. Enthalpy
C. Gibbs energy
D. Internal energy

Correct Answer: B. Enthalpy

Solution:
Enthalpy is represented by H and is defined as:

H = U + PV

At constant pressure, the change in enthalpy is related to the heat absorbed or released by the system.

Therefore, the correct answer is Enthalpy.

Question 9: Which element has the highest electronegativity?

A. Oxygen
B. Nitrogen
C. Fluorine
D. Chlorine

Correct Answer: C. Fluorine

Solution:
Electronegativity generally increases from left to right across a period and decreases down a group.

Fluorine has the highest electronegativity among all elements.

Question 10: Which type of isomerism occurs when a ligand can coordinate to a metal through two different atoms?

A. Ionisation isomerism
B. Linkage isomerism
C. Coordination isomerism
D. Geometrical isomerism

Correct Answer: B. Linkage isomerism

Solution:
Some ligands can attach to a metal through different donor atoms. Such ligands are called ambidentate ligands.

For example, NO₂⁻ can coordinate through nitrogen or oxygen.

This gives rise to linkage isomerism.

MET Mathematics Most Repeated Questions

Question 1: A bag contains 3 red, 4 white and 5 blue balls. Two balls are drawn at random. What is the probability that the two balls are of different colours?

A. 19/66
B. 47/66
C. 31/66
D. 23/66

Correct Answer: B. 47/66

Solution:
Total balls = 12

Total ways of selecting two balls:

12C2 = 66

Ways of selecting balls of the same colour:

3C2 + 4C2 + 5C2

= 3 + 6 + 10

= 19

Ways of selecting balls of different colours:

66 − 19 = 47

Therefore: Probability = 47/66

Question 2: If the roots of $x^3+p x^2+q x+r=0$ are in geometric progression, which relation is satisfied by p, q and r?

A. q³ = rp³
B. p³ = qr²
C. q² = pr
D. p² = qr

Correct Answer: A. q³ = rp³

Solution:
Let the roots be a/d, a and ad.

Using the relations between roots and coefficients:

Sum of roots = −p

Sum of products of roots taken two at a time = q

Product of roots = −r

From the first two relations:

a = −q/p

Since the product of roots is:

a³ = −r

Substituting a = −q/p:

(−q/p)³ = −r

Therefore: q³ = rp³

Question 3: A vertex of a square is (−4, 5), and one diagonal is $7 x-y+8=0$. Find the equation of the other diagonal.

A. $x+7 y-31=0$
B. $7x + y − 31 = 0$
C. $x − 7y + 31 = 0$
D. $7x − y + 31 = 0$

Correct Answer: A. $x + 7y − 31 = 0$

Solution:
Given line:

$7x − y + 8 = 0$

or

$y = 7x + 8$

Its slope is 7.

Since the diagonals of a square are perpendicular:

Required slope = -1/7

Using point (-4, 5):

$y-5=-1 / 7(x+4)$

After simplifying:

$x+7 y-31=0$

Question 4: Find the mean deviation about the median for the observations 20, 33, 39, 40, 50, 53, 59, 65 and 69.

A. 10.67
B. 11.67
C. 12.67
D. 13.67

Correct Answer: C. 12.67

Solution:
There are 9 observations.

Therefore, the median is the fifth observation:

Median = 50

Absolute deviations from 50 are:

30, 17, 11, 10, 0, 3, 9, 15, 19

Sum = 114

Mean deviation = 114/9

= 12.67

Question 5: A man walks 10 metres towards a tower. At the first position, the angle of elevation of the top of the tower is 30°. At the second position, it becomes 60°. What is the distance of the man from the tower at the second position?

A. 2.5 m
B. 5 m
C. 10 m
D. 15 m

Correct Answer: B. 5 m

Solution:
Let the distance from the second position to the tower be x.

Distance from the first position = x + 10.

Using the tangent ratios:

$\tan 30^{\circ}=h /(x+10)$

$\tan 60^{\circ}=\mathrm{h} / \mathrm{x}$

Since $\tan 30^{\circ}=1 / \sqrt{ } 3$ and $\tan 60^{\circ}=\sqrt{ } 3$ :

$\frac{x+10}{\sqrt{3}}=x\sqrt{3}$

$x+10=3x$

$2x=10$

Therefore: x = 5 m

Question 6: If A is a square matrix and |A| = 0, which statement is correct?

A. A is always an identity matrix
B. A is a singular matrix
C. A is always an orthogonal matrix
D. A is an invertible matrix

Correct Answer: B. A is a singular matrix

Solution:
A square matrix is singular when its determinant is zero.

Given:

|A| = 0

Therefore, A is a singular matrix and does not have an inverse.

Question 7: For what value of k will the equation $x^2-4 x+k=0$ have equal roots?

A. 2
B. 4
C. 8
D. 16

Correct Answer: B. 4

Solution:
For equal roots, the discriminant must be zero.

For $a x^2+b x+c=0$ :

$D=b^2-4 a c$

Here:

$a=1, b=-4 \text { and } c=k$

Therefore:

$D=16-4 \mathrm{k}$

For equal roots:

$16-4k=0$

$4k=16$

$k=4$

Question 8: What is the value of $\sin 30^{\circ}+\cos 60^{\circ}$?

A. 0
B. 1/2
C. 1
D. $\sqrt{ } 2$

Correct Answer: C. 1

Solution:

$\sin 30^{\circ}=1 / 2$

$\cos 60^{\circ}=1 / 2$

Therefore:

$\sin 30^\circ+\cos 60^\circ$

$=\frac{1}{2}+\frac{1}{2}$

$=1$

Question 9: A coin is tossed three times. What is the probability of getting exactly two heads?

A. 1/8
B. 3/8
C. 1/2
D. 5/8

Correct Answer: B. 3/8

Solution:
Total possible outcomes:

$2^3=8$

The outcomes with exactly two heads are:

HHT, HTH and THH

Number of favourable outcomes = 3

Therefore:

Probability = 3/8

Question 10: If $y=x^3-3 x^2+2 x$, what is dy/dx?

Options:

A. $3 \mathrm{x}^2-6 \mathrm{x}+2$

B. $3 \mathrm{x}^2-3 \mathrm{x}+2$

C. $x^2-6 x+2$

D. $3 \mathrm{x}^2-6 \mathrm{x}$

Correct Answer: A. $3 \mathrm{x}^2-6 \mathrm{x}+2$

Solution:

Given:

$y=x^3-3 x^2+2 x$

Differentiating with respect to $x$ :

$\mathrm{dy} / \mathrm{dx}=3 \mathrm{x}^2-6 \mathrm{x}+2$

Therefore: $d y / d x=3 x^2-6 x+2$

MET 2027 Exam Pattern and Marking Scheme

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MET Mock Test 2027

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